Synchronization dynamics of modified relay-coupled chaotic systems

Abstract

In this manuscript, we study the dynamics of a modified relay-coupled chaotic systems. The modification consists on the fact that the relay unit is modeled to lead the entire network to a desired dynamics. Then we achieve finite-time synchronization indirectly through a linear combination of the three systems. Further, we consider the existence of a switch on time of the coupling from the relay unit to the outer systems. It appears some interesting behaviors such as bifurcations, alternation of crisis and phases transitions when varied the switch on time. An open result is also found. In our scheme and for the selected changeable initial conditions, it seems that the appearance or disappearance of coexistence of attractors is linked to the type of synchronization we are dealing with. Mathematical demonstrations are given to sustain our theory while numerical simulations show its effectiveness.